This invention relates to attitude control systems for spacecraft using reaction wheels, and more particularly to reduction in attitude errors during times when the wheel speed is reduced to zero and the direction of rotation is reversed.
Spacecraft have become important as platforms for communications or sensors. As a platform, the position or attitude of the spacecraft in space must be maintained constant relative to a distant object, such as the heavenly body which it orbits. In the absence of stabilization of the attitude of the spacecraft, the sensors or communication devices cannot be pointed in the desired direction with the desired accuracy.
Certain types of spacecraft are stabilized by spinning about an axis. With such spacecraft, the attitude of the spacecraft in inertial space remains essentially constant. While this may be desirable when a sensor is to be directed along its axis toward a distant inertially fixed target such as a star, it is less advantageous when directing an instrument towards a target moving relative to the spacecraft (i.e., on the Earth). The use of despun platforms on spin-stabilized spacecraft allow instruments or antennas to be pointed in directions other than along the spin axis. However, because the attitude of a spin-stabilized spacecraft remains constant in inertial space as the spacecraft orbits the Earth, constant articulation is required to orient the platform toward a point on Earth, which may be undesirable for some purposes.
The attitude of some spacecraft may be maintained by controlled firing of attitude control thrusters, as described in U.S. Pat. No. 3,866,025, issued Feb. 11, 1975 to Cavanagh. Such systems if used alone tend to be short-lived because the amount of expendable fuel is finite.
Magnetic torquers may be used for attitude control, as also described by Cavanagh. Current is allowed to flow through torquing coils located on the spacecraft body, to cause interaction with the Earth's magnetic field. Magnetic torquing cannot produce large torques for fast correction of attitude errors because the Earth's magnetic field in space is small in magnitude and uncertain in direction.
Spacecraft may also be stabilized by the use of one or more momentum or reaction wheels, either alone or in conjunction with thrusters and/or magnetic torquers. A common arrangement includes the use of three or more reaction wheels, whose axes are orthogonal, or at angles that provide components along the three orthogonal spacecraft axes, thereby providing three-axis control of the spacecraft attitude. Such a system is described in U.S. Pat. No. 3,999,729 issued Dec. 28, 1976 to Muhlfelder et al. It should be noted that momentum wheels differ from reaction wheels only in that they are operated at rotational speeds which are high enough to provide gyroscopic stiffness. Momentum wheels are not ordinarily reduced to near-zero speed, as are reaction wheels.
As described at length in U.S. Pat. No. 3,998,409 issued Dec. 21, 1976 to Pistiner, the roll and yaw axis reaction wheels of a three-axis momentum stabilized spacecraft interchange their stored angular momentum on a quarter-orbit basis. As a result, the roll and yaw axis reaction wheels reverse their speed directions twice per orbit. Attitude sensors on the spacecraft sense the attitude of the spacecraft and produce error signals equal to, or representative of the difference between the actual spacecraft attitude and its desired attitude. These error signals are integrated and are converted into appropriate torque command signals for each reaction wheel. The resulting reaction wheel rotations produce reaction torques on the spacecraft that reduce its attitude error. The bearings supporting the reaction wheel's rotation ordinarily are of very high quality, but are subject to frictional forces. FIG. 1 illustrates a spacecraft 10 using a reaction wheel 12 affixed to an axle 14 mounted on bearings 16 supported by bearing blocks 18 and 20. A motor or torquer 22 is coupled to wheel 12 for applying torque to the wheel under control of a torque command signal applied over a bus 24 from a control unit 26. Control unit 26 generates the torque command signal based upon an attitude error signal applied over a bus 28 from an attitude sensor 30. Attitude sensor 30 senses errors in the attitude of the body of spacecraft 10 about wheel axis 8. When the wheel is rotating, the bearing friction includes a fluid friction component that increases with increasing velocity. Another component of friction is the Coulomb component, which is constant and independent of speed. FIG. 2 plots as 40 the torque T necessary to overcome Coulomb friction versus angular speed .omega. for a wheel such as 12 of FIG. 1. At positive values of .omega., the torque T has a positive value and for negative .omega. (the opposite direction of rotation), T has the same magnitude, but in the opposite direction. The constant component of Coulomb friction therefore exists down to and including zero rotational velocity. Static friction, which causes an increase in the force required to break the bearings away from a static or nonmoving condition, is generally small in the high quality bearings ordinarily used in conjunction with spacecraft reaction wheels. Static friction is suggested by dotted curve 42.
FIG. 3 illustrates, in simplified block diagram form, the control scheme described in the Pistiner patent. In FIG. 3, elements corresponding to those of FIG. 1 are designated by the same reference numeral. A spacecraft illustrated by the system of FIG. 3 uses attitude sensors and an integrator to produce a torque command signal on bus 24 for driving torquer 22 and reaction wheel 12. In order to control the attitude error on bus 28 to zero, the integrated error signal on bus 24 (which is the torque command signal) must be large enough to overcome the constant frictional force attributable to the Coulomb friction of the bearing. Thus, as the wheel slows toward and reaches zero speed, the torque command signal still has a finite value which represents the amount of the torque command signal required to overcome the Coulomb friction while the wheel rotates. When the reaction wheel stops, the attitude of the spacecraft about the wheel axis is no longer controlled, and attitude errors of spacecraft 10 can begin to accumulate. The attitude errors are sensed by sensor 30 and an error signal is produced and applied over bus 28 to integrator 60 of FIG. 3. Attitude errors continue to accumulate while the wheel is stopped, because the error signals must be applied to the integrator for a finite length of time in order to first reduce the residual (Coulomb-attributable) component of torque command signal to zero, and then to increase the torque command signal to a value sufficient to overcome the Coulomb and static friction required for rotation in the opposite direction. The torques required for rotation are illustrated in FIG. 2. During the period of integration, the attitude error tends to increase, and therefore the sensed error signal increases more than it would if attitude control were continuous and Coulomb friction were absent. Consequently, at the moment when reaction wheel rotation in the opposite direction begins, the error signal tends to be larger than necessary, and as a result the torque command signal is excessive. This overly large torque command signal in turn causes an overcompensation for the accumulated attitude error. Thus, in the absence of compensation for Coulomb friction, large attitude errors may be expected. FIG. 4 illustrates as a plot 70 the reaction wheel speed time history. In FIG. 4, the wheel speed is decreasing linearly toward zero speed before time T1. Ideally, the direction of rotation should simply reverse, and the wheel speed should increase in the opposite direction, as illustrated by dotted line 71. Due to Coulomb and static friction, the wheel remains stopped in the interval from time T1 until time T2. During this time, the control circuit reverses the torque command signal and increases its magnitude, until the torque is sufficient to overcome bearing friction at time T2, and the wheel then accelerates. At time T2, however, the torque command signal is large enough to cause a temporary overcorrection or overshoot of the path it would follow in the absence of friction illustrated as a curved portion 72 of plot 70.
FIG. 5a is a plot of the results of a computer simulation of the attitude error and wheel speed of a spacecraft using reaction wheel attitude control without Pistiner's correction. Dotted curve 80 represents wheel speed, which reverses direction of about 1000 seconds. Solid-line plot 82 represents the attitude error. As illustrated, the effects of reaction-wheel bearing friction result in a peak attitude error of about 52 arc-seconds in the interval 1000 seconds to about 1020 seconds, during which time the reaction wheel is stopped. Immediately after 1020 seconds, the wheel accelerates, and a recovery attitude undershoot of eight arc-seconds occurs.
The Pistiner arrangement recognizes that the integrator output signal includes information relating to the magnitude of the Coulomb friction. In the Pistiner arrangement, an offset signal compensator illustrated in FIG. 3 as block 52 generates an offset signal which is applied to an adder 54 and summed with the torque command signal to overcome the Coulomb friction. The magnitude of the offset is established by sensing the wheel rotational speed by a sensor 50, noting the magnitude of the torque command signal at some wheel rotational speed in the range of 5 to 10 RPM, and performing calculations which are intended to subtract out the components which are attributable to known factors, such as orbital precession torques, whereupon the remaining magnitude of the torque command signal is assumed to correspond to value +T.sub.c of FIG. 2, the Coulomb attributable friction torque. Once the magnitude of the component of the torque command signal attributable to the Coulomb bearing friction is found, its value is doubled to 2T.sub.c (since the value must be reduced to zero and then increased back to the same value in the opposite direction), inverted in phase (-2T.sub.c) and then added (in summer 54) to the torque command signal. When - 2T.sub.r is summed with a torque command signal including a component of +T.sub.c, the resulting summed torque command signal includes a reversed component with an amplitude -T.sub.c, which is exactly what is necessary to overcome the Coulomb friction when wheel reversal takes place. This technique is effective in reducing attitude errors. FIG. 5b illustrates the improved spacecraft attitude response when offset compensation is used in the Pistiner manner. FIG. 5b is similar to FIG. 5a, and corresponding plots are designated by the same reference numerals. As illustrated in FIG. 5b, the wheel speed represented by dashed line 80, while not stopped for a sustained period near 1000 seconds as in the uncompensated case of FIG. 5a, is nevertheless perturbed. The spacecraft attitude builds up to an error of about 10 arc-seconds. This occurs because the offset does not exactly cancel the actual reaction wheel friction. In the Pistiner arrangement, integrated error signal components attributable to sources which are not taken into account in the offset calculation will result in an incorrectly calculated torque command signal Such errors might arise due to environmental or internal disturbance forces an torques active on the spacecraft. Also, the effective reversal of T.sub.c at a wheel rotational velocity of .omega.=10 RPM itself tends to perturb the attitude, by slowing the wheel by more than the expected amount, which again contributes to attitude error.
If the offset signal which is added to the torque command signal in the Pistiner arrangement deviates in magnitude from the true value required for the overcoming of friction, the result will be similar to that which occurred in the absence of compensation, namely attitude errors due to undercompensation or overcompensation. An improved reaction wheel attitude control arrangement is desired.